Definitely do not use the Fullscreen option in EA.
I have a laptop and 1 external monitor. I had to set the game up to run on the external monitor, That allows me to use the laptop screen for anything else and it does not black out the game or vice versa when I switch screens.
I run that monitor at 1920x1080 - yours may be different. That aspect ratio (16:9) cuts off part of the top of the view when playing - so it is not ideal. The 4:3 aspect ratio (1024x768) shows all of the view - but does not use my full screen with.
BTW Scott - Up until recently I had to use the resizer every time I opened EA, but apparently that glitch has been fixed (probably while they were trying to do something else).
I hope this helps. GL.